The present invention pertains generally to devices and methods for producing and processing plasmas. More particularly, the present invention pertains to a device for preventing plasma loss through one end of a cylindrical plasma chamber. The present invention is particularly, but not exclusively, useful as a device that is positionable at one end of a plasma mass filter and which uses ponderomotive forces to direct plasma particles away from the end of the plasma mass filter.
It is well known that the orbital motions of charged particles (ions and electrons) in a magnetic field, or in crossed electric and magnetic fields, will differ from each other according to their respective mass to charge ratio. Thus, when the probability of ion collision is significantly reduced, ions can be separated according to their respective mass to charge ratio. For example, U.S. Pat. No. 6,096,220, which issued on Aug. 1, 2000 to Ohkawa, for an invention entitled xe2x80x9cPlasma Mass Filterxe2x80x9d and which is assigned to the same assignee as the present invention, discloses a device which relies on the different, predictable, orbital motions of charged particles in crossed electric and magnetic fields in a plasma chamber to separate the charged particles from each other.
In the filter disclosed in Ohkawa ""220, a multi-species plasma is introduced into one end of a cylindrical chamber for interaction with crossed electric and magnetic fields. As further disclosed in Ohkawa ""220, the fields can be configured to cause ions having relatively high-mass to charge ratios to be placed on unconfined orbits. These ions are directed towards the cylindrical wall for collection. On the other hand, ions having relatively low-mass to charge ratios are placed on confined orbits inside the chamber. These ions transit through the chamber toward the ends of the chamber. It can happen, however, that some low-mass ions are directed toward the end where the multi-species plasma is being introduced into the chamber. This allows the low-mass ions to be re-mixed with multi-species plasma, lowering the energy efficiency of the plasma mass filter since these light ions will be reionized and reprocessed.
One way to overcome the end loss described above is to use a tandem plasma mass filter. Specifically, U.S. Pat. No. 6,235,202, which issued on May 22, 2001 to Ohkawa, for an invention entitled xe2x80x9cTandem Plasma Mass Filterxe2x80x9d and which is assigned to the same assignee as the present invention, discloses a device wherein the feed material is introduced midway between the ends of a cylindrical plasma chamber. After separation in the plasma chamber, the light ions are collected at both ends of the cylindrical chamber. Because a plasma needs to be created near the center of the plasma chamber, the tandem mass filter requires a high density vapor jet or some other injector to introduce vapor into the chamber. Once the vapor is introduced into the chamber, an r-f antenna or some other mechanism is required to heat and ionize the vapor. The present invention solves the end loss problem in a different way than the tandem plasma mass filter. Specifically, the present invention contemplates the use of r-f ponderomotive forces to prevent plasma particles in a cylindrical plasma chamber from reaching one end of a plasma chamber. At the same time, the present invention allows for a multi-species plasma to be introduced into the plasma chamber from the end, for example with a diffuse vapor source.
It is well known that photons carry momentum. When a photon is either reflected from a media or absorbed by the media, momentum is transferred from the photon to the medium. Importantly, this momentum transfer exerts a force on the medium. In the case where the medium is a plasma, a force is exerted on the particles (ions and electrons) in the plasma. The force imparted on the media (plasma) during photon absorption is relatively small because the momentum of photons is relatively small per their energy (i.e. the momentum of photons is their energy divided by the velocity of light (c)). The power flux, P, of photons required to exert a pressure, p, on the medium via photon absorption is given by P=p c. Thus, to generate a pressure of 1 pascal using photon absorption requires approximately 300 MW/m2 of power flux. Unfortunately, this level of power flux is, for all practical purposes, impossible to implement. An additional drawback associated with the use of photon absorption to impart a force on a media is that each photon can only be used once to impart a force. This is because upon absorption of the electromagnetic wave by the media (i.e. plasma), the wave is dissipated and cannot be reused.
When a wave of photons (i.e. an electromagnetic wave) is evanescent in a medium, reflection of the wave occurs. Unlike absorption, in the case of reflection, the photon energy is not lost. Rather, the photons can be reused by simply redirecting the reflected photons, again and again. For example, an r-f cavity can be used to redirect the reflected photons. For an r-f cavity, the number of reflections is equal to the Q-value of the cavity, and the power, P, required to exert a pressure, p, on the medium becomes
P=pc/Q.xe2x80x83xe2x80x83[1] 
For Q=1000, a pressure of 1 pascal requires a power of approximately 0.3 MW/m2. Thus, it is much more efficient to use photon reflection (by using an electromagnetic wave that is evanescent in a magnetized plasma) than photon absorption to generate ponderomotive forces on a plasma.
In a uniform, stationary magnetic field, the ions and electrons in a plasma will rotate in oppositely directed orbits. If a circularly polarized electromagnetic wave is propagating in the direction of the magnetic field, two distinct circular polarizations are possible; right-hand polarized and left-hand polarized. In the right-hand polarized wave, the electric field rotates in the same direction as the gyration of the electrons in the stationary magnetic field. In contrast, in the left-hand polarized wave, the electric field rotates in the opposite direction as the gyration of the electrons in the stationary magnetic field.
From the dispersion relationship, it can be determined whether a wave will be evanescent in a selected media. For example, the dispersion of the left-hand polarized wave in a plasma is given by
k2=cxe2x88x922{xcfx892-xcfx89p2[1+xcexa9e/xcfx89]xe2x88x921}xe2x80x83xe2x80x83[2a] 
where k is the wave number, xcfx89 is the frequency, xcfx89p is the plasma frequency xcfx89p={square root over (ne2/Eome)} and xcexa9e is the electron cyclotron frequency xcexa9e=xe2x88x92eB/me. Similarly, the dispersion of the right-hand circularly polarized wave in a plasma is given by
k2 =cxe2x88x922{(xcfx892-xcfx89p2[1xe2x88x92xcexa9e/xcfx89]xe2x88x921}xe2x80x83xe2x80x83[2b] 
Thus, the right-hand circularly polarized wave is propagating if xcfx89 less than xcexa9e while the left-hand circularly polarized wave is evanescent if
xcfx89 less than [xcfx89p2+xcexa9e2/ 4]1/2xe2x88x92xcexa9e/2.xe2x80x83xe2x80x83[3] 
Thus, a left-hand circularly polarized wave having (o as indicated in equation [3] is evanescent and can be used to establish a ponderomotive force via photon reflection. One example of a right-hand circularly polarized wave is a helicon wave with azimuthal mode number, I=1.
Consider now a circularly polarized TE11 mode electromagnetic wave in a circular wave guide. The dispersion for both polarizations is given by
k2=xcfx892(c2=xcex2xe2x80x83xe2x80x83[4] 
where xcex=xcex5/a, xcex5 is the first null of the first order Bessel Function derivative, J1xe2x80x2, and a is the radius of the guide. Importantly, the wave is evanescent if xcfx89 less than cxcex. The analysis below shows that the evanescence produced by the circular wave guide is just as effective as the plasma induced evanescence in exerting the ponderomotive force on charged particles. Furthermore, as the density of charged particles is increased, the dispersion changes from the dispersion in vacuum. The ponderomotive force, however, is present as long as the evanescence is maintained.
Consider now the motion of a charged particle with charge, q, and mass, M, under the electric field given by
Ex+iEy=E exp[xe2x88x92ixcfx89t+kz].xe2x80x83xe2x80x83[5] 
The magnetic field is given by
Bx+iBy=[xcfx89/k]E exp[xe2x88x92ixcfx89t+kz]. xe2x80x83xe2x80x83[6] 
The equations of motion become
M d vx/dt=q Ex+q vyBo 
M d vy/dt=q Eyxe2x88x92q vxBo 
M d vz/dt=Fz=q [VxByxe2x88x92vyBx] [7] 
from which the following relationships are obtained
vx+i vy=xe2x88x92i[q/M] [xe2x88x92xcfx89+xcexa9]xe2x88x921 E exp[xe2x88x92ixcfx89t+kz] xe2x80x83xe2x80x83[8] 
Fz=[k q2/M xcfx89] [xe2x88x92xcfx89+xcexa9]xe2x88x921E2exp [2 kz] xe2x80x83xe2x80x83[9] 
where xcexa9 is the cyclotron frequency, including the sign.
If the sign of Bo is chosen so that xcexa9e less than 0 and xcexa9i greater than 0, then the ponderomotive force on the electrons and ions is negative for xcfx89 greater than xcexa9i. Thus, they are both repelled from the stronger field region. The magnitude of the electric field necessary to stop the electron of energy Te is given by
E2=xcfx89Bo[Te/e] xe2x80x83xe2x80x83[10] 
with xcfx89=109/s, Bo=0.1 T and Te=1 eV, the field is 104 V/m.
The response of the plasma is obtained by multiplying the plasma density, n, to eq [8],
jx+ijy=xe2x88x92i[q2n/ m] [xe2x88x92xcfx89+xcexa9]xe2x88x921 E exp [xe2x88x92ixcfx89t+k z]. xe2x80x83xe2x80x83[11] 
The contributions from the electrons and the ions must be added. Similarly, the total ponderomotive force is obtained by summing equation [9] for all charged particles.
We define the ponderomotive potential U by
∂U/∂z=xe2x88x92Fzxe2x80x83xe2x80x83[12]
so the potential is independent of k as long as the maximum value of E is fixed. Thus, it takes as much electric field to repel a single electron as the plasma electrons. It is contemplated that the negative value of the plasma dielectric constant causes the total pressure to be the kinetic pressure minus the electric stress. In situations where the radial mode number is not zero, modes with many different k""s can propagate and the matching requires summary over all k""s.
In light of the above, it is an object of the present invention to provide a device that is positionable at one end of a plasma mass filter which uses ponderomotive forces to direct the plasma particles away from the end of the plasma mass filter. It is another object of the present invention to provide a plasma mass filter having improved separation efficiency and reduced end loss. It is yet another object of the present invention to provide a device for a plasma mass filter that reduces end loss and allows for the plasma to be introduced into the chamber with a diffuse vapor source. Yet another object of the present invention is to provide an end plug for a plasma mass filter which is easy to use, relatively simple to implement, and comparatively cost effective.
The present invention is directed to a device and method for preventing plasma loss through one end of a cylindrical plasma chamber. In the preferred embodiment, the present invention can be used in conjunction with a plasma mass filter to increase the energy efficiency of the filter. In accordance with the present invention, this is achieved by preventing plasma particles as they undergo separation from returning to the end of the cylindrical chamber where the feed for the plasma is being introduced into the chamber. To prevent the plasma particles from returning to the end of the chamber, an electromagnetic wave having specific characteristics is launched into the plasma to generate ponderomotive forces on the plasma particles. Specifically, in accordance with the mathematical calculations set forth above, the electromagnetic wave has two important characteristics for the present invention. First, the electromagnetic wave must be evanescent in the plasma. Second, the electromagnetic wave must have a frequency, xcfx89, which is greater than the ion cyclotron frequency in the plasma, xcexa91. As further indicated above, such an electromagnetic wave can be established using a cylindrical wave guide.
In the preferred embodiment of the present invention, the plasma chamber includes a cylindrical wave guide to surround a plasma. The cylindrical wave guide of radius, a, is centered along a longitudinal axis and is formed with a first open end for receiving a multi-species plasma and a second end to allow plasma particles to exit. For the case where the present invention is used in conjunction with a plasma mass filter, E x B separation is accomplished within the cylindrical wave guide. In any case, coils are provided to generate a substantially uniform magnetic field having a magnitude B in the plasma chamber (i.e. in the wave guide). Preferably, the magnetic field is oriented substantially along the longitudinal axis of the wave guide. With this magnetic field, ions and electrons in the plasma rotate at respective cyclotron frequencies xcexa9e and xcexa9i.
An antenna is provided to launch an electromagnetic wave into the wave guide through the first end of the wave guide. The electromagnetic wave is preferably launched substantially in the direction of the magnetic field (i.e. axially). Specifically, the antenna is preferably configured relative to the wave guide to launch an electromagnetic wave that will create a circularly polarized TE11 mode electromagnetic wave in the wave guide. Furthermore, the circularly polarized electromagnetic wave that is created in the wave guide preferably has a frequency xcfx89, wherein xcfx89 less than cxcex5/ a, with c being the speed of light and xcex5 being the null of the first order Bessel Function derivative J1"" of the wave guide. Additionally, for the present invention, the antenna is configured to produce a circularly polarized electromagnetic wave in the wave guide having an E vector that rotates at frequency, xcfx89, in a direction opposite to the direction of electron rotation in the plasma (i.e. left-hand circularly polarized wave). As such, the electromagnetic wave will be evanescent in the wave guide and impart a ponderomotive force on the plasma particles. To impart a confining ponderomotive force (i.e. a force directed towards the second end of the wave guide) on both the ions and the electrons, the frequency, xcfx89, of the electromagnetic wave is chosen to be greater than the ion cyclotron frequency, xcexa9i.
As indicated in the discussion above, because the electromagnetic wave is evanescent in the wave guide, the wave will be reflected from the plasma, producing a reflected wave that is directed back toward the first end of the wave guide. For the present invention, a resonance cavity is provided to then redirect the reflected photons back into the plasma. To accomplish this, the resonance cavity includes a cylindrical wave guide having a reflective endpiece at one end. The other end of the resonant cavity is attached to the first end of the plasma chamber wave guide (i.e. the wave guide that surrounds the plasma). This results in a combination of structure that allows the electromagnetic waves to travel back and forth between the plasma and the reflective endpiece. Each time the wave reflects from the plasma, a ponderomotive force is imparted on the plasma particles. Because the wave is required to propagate in the resonance chamber, the resonance chamber wave guide is dimensioned to ensure the wave is above the cutoff frequency for the resonance chamber wave guide. Alternatively, if it is desired to have equal diameters for the resonance chamber wave guide and the plasma chamber wave guide, the resonance chamber wave guide can be filled with a suitable dielectric to ensure the wave propagates in the resonance chamber wave guide and is evanescent in the plasma chamber wave guide.